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Resources tagged with Generalising similar to Steps to the Podium:

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There are 141 results Steps to the Podium

Age 7 to 14 Challenge Level:

It starts quite simple but great opportunities for number discoveries and patterns! Number Pyramids

Age 11 to 14 Challenge Level:

Try entering different sets of numbers in the number pyramids. How does the total at the top change? Window Frames

Age 5 to 14 Challenge Level:

This task encourages you to investigate the number of edging pieces and panes in different sized windows. Keep it Simple

Age 11 to 14 Challenge Level:

Can all unit fractions be written as the sum of two unit fractions? Go Forth and Generalise

Age 11 to 14

Spotting patterns can be an important first step - explaining why it is appropriate to generalise is the next step, and often the most interesting and important. Nim-7

Age 5 to 14 Challenge Level:

Can you work out how to win this game of Nim? Does it matter if you go first or second? Shear Magic

Age 11 to 14 Challenge Level:

What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles? Magic Letters

Age 11 to 14 Challenge Level:

Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws? Picturing Triangular Numbers

Age 11 to 14 Challenge Level:

Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers? Age 11 to 14 Challenge Level:

Great Granddad is very proud of his telegram from the Queen congratulating him on his hundredth birthday and he has friends who are even older than he is... When was he born? Triangle Numbers

Age 11 to 14 Challenge Level:

Take a look at the multiplication square. The first eleven triangle numbers have been identified. Can you see a pattern? Does the pattern continue? Age 11 to 14 Challenge Level:

Think of a number, add one, double it, take away 3, add the number you first thought of, add 7, divide by 3 and take away the number you first thought of. You should now be left with 2. How do I. . . . Regular Hexagon Loops

Age 11 to 14 Challenge Level:

Make some loops out of regular hexagons. What rules can you discover? Enclosing Squares

Age 11 to 14 Challenge Level:

Can you find sets of sloping lines that enclose a square? Age 11 to 14 Challenge Level:

List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it? Make 37

Age 7 to 14 Challenge Level:

Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37. Dicing with Numbers

Age 11 to 14 Challenge Level:

In how many ways can you arrange three dice side by side on a surface so that the sum of the numbers on each of the four faces (top, bottom, front and back) is equal? Hidden Rectangles

Age 11 to 14 Challenge Level:

Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard? One O Five

Age 11 to 14 Challenge Level:

You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . . Cubes Within Cubes Revisited

Age 11 to 14 Challenge Level:

Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need? Handshakes

Age 11 to 14 Challenge Level:

Can you find an efficient method to work out how many handshakes there would be if hundreds of people met? Chocolate Maths

Age 11 to 14 Challenge Level:

Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . . ...on the Wall

Age 11 to 14 Challenge Level:

Explore the effect of reflecting in two intersecting mirror lines. Christmas Chocolates

Age 11 to 14 Challenge Level:

How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes? Partitioning Revisited

Age 11 to 14 Challenge Level:

We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4 Who Is the Fairest of Them All ?

Age 11 to 14 Challenge Level:

Explore the effect of combining enlargements. Age 11 to 14 Challenge Level:

A little bit of algebra explains this 'magic'. Ask a friend to pick 3 consecutive numbers and to tell you a multiple of 3. Then ask them to add the four numbers and multiply by 67, and to tell you. . . . More Number Pyramids

Age 11 to 14 Challenge Level:

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge... Egyptian Fractions

Age 11 to 14 Challenge Level:

The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions. Sum Equals Product

Age 11 to 14 Challenge Level:

The sum of the numbers 4 and 1 [1/3] is the same as the product of 4 and 1 [1/3]; that is to say 4 + 1 [1/3] = 4 � 1 [1/3]. What other numbers have the sum equal to the product and can this be so for. . . . How Much Can We Spend?

Age 11 to 14 Challenge Level:

A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know? Searching for Mean(ing)

Age 11 to 14 Challenge Level:

Imagine you have a large supply of 3kg and 8kg weights. How many of each weight would you need for the average (mean) of the weights to be 6kg? What other averages could you have? What Numbers Can We Make Now?

Age 11 to 14 Challenge Level:

Imagine we have four bags containing numbers from a sequence. What numbers can we make now? Cuboid Challenge

Age 11 to 16 Challenge Level:

What's the largest volume of box you can make from a square of paper? Three Times Seven

Age 11 to 14 Challenge Level:

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why? Mini-max

Age 11 to 14 Challenge Level:

Consider all two digit numbers (10, 11, . . . ,99). In writing down all these numbers, which digits occur least often, and which occur most often ? What about three digit numbers, four digit numbers. . . . Picturing Square Numbers

Age 11 to 14 Challenge Level:

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153? Special Sums and Products

Age 11 to 14 Challenge Level:

Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48. Games Related to Nim

Age 5 to 16

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning. Route to Infinity

Age 11 to 14 Challenge Level:

Can you describe this route to infinity? Where will the arrows take you next? Consecutive Negative Numbers

Age 11 to 14 Challenge Level:

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers? Frogs

Age 11 to 14 Challenge Level:

How many moves does it take to swap over some red and blue frogs? Do you have a method? Tourism

Age 11 to 14 Challenge Level:

If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable. Konigsberg Plus

Age 11 to 14 Challenge Level:

Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges. Tilted Squares

Age 11 to 14 Challenge Level:

It's easy to work out the areas of most squares that we meet, but what if they were tilted? Nim-like Games

Age 7 to 16 Challenge Level:

A collection of games on the NIM theme Nim-interactive

Age 11 to 16 Challenge Level:

Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The winner is the player to take the last counter. Winning Lines

Age 7 to 16

An article for teachers and pupils that encourages you to look at the mathematical properties of similar games. Sliding Puzzle

Age 5 to 16 Challenge Level:

The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves. 2001 Spatial Oddity

Age 11 to 14 Challenge Level:

With one cut a piece of card 16 cm by 9 cm can be made into two pieces which can be rearranged to form a square 12 cm by 12 cm. Explain how this can be done.